Thursday, May 18, 2006

Piling on the tetrapods

Here are three great tastes that taste great together: Balaenoptera musculus, Brachiosaurus altithorax, and Loxodonta africana. Plus Mike and me for scale. Many thanks to Photoshop for making this happy day possible.

The elephant and brachiosaur are both from the Field Museum in Chicago. Mike and I spent some quality time with them last summer, especially the Brachiosaurus skeleton. It is outdoors, so we could roam around it to our hearts' content, from the time the museum closed until it got too dark to see. One of the things we were trying to figure out is, how much might that animal have weighed?

This is not a trivial problem. Weighing large extant animals is no picnic. Almost all of the heights and weights of big elephants are to some extent estimates. When you shoot an elephant and it flops over, you can measure its length very accurately, but its giant body is no longer being compressed by gravity in the foot-to-shoulder axis and it stretches out some. Also, world record elephants tend to be shot out in the bush, very far from things like truck scales that would allow for accurate weight measurements. Usually the body is hacked up and weighed piecemeal, but there is some inevitable blood loss and so the summed weight of the chunks is not the weight of the animal in life. For both height and weight, a little guesswork is needed to figure out what the real measurement ought to be. The world record elephant was 13'8" lying on its side, and it is estimated to have been about 13'0" when standing. Conveniently, it weighed about 13 tons (these numbers are from the Guinness Book).

Now, using Photoshop and our not-yet-patented "stack of Mike" method, we pegged the mounted bull shown above with a shoulder height of 10 feet. In his paper on dinosaur models, Greg Paul (1997) cites a personal communication from someone at the Field Museum with the information that this animal weighed six tons. Because mass scales with the cube of the linear dimension, a 13-foot-tall elephant should weigh 2.2 times as much as a 10-footer, and indeed, 6 x 2.2 = 13.

One thing that occurred to us was to treat Brachiosaurus like a giant elephant. Brachiosaurus has a long pneumatic neck and the elephant has a big pneumatic head, so you can think of both of them as having a big air-filled mass of bone hanging off the front of their shoulders. In his book A Practical Guide to Vertebrate Mechanics, Chris McGowan gives some figures on a big bull elephant named Tantor. Tantor massed 6500 kg and his head was 750 kg, or a shade over 10% of his total mass. In the same paper mentioned above, Paul (1997) said that in sauropods the neck and head accounted for about 10% of the volume. So our elephant head/sauropod neck comparison is not completely retarded. The sauropod's tail is a bigger problem, but it probably only accounted for about 5% of the animal's mass, and the "stack of Mike" method is sufficiently non-rigorous for 5% error to be acceptable. On the flip side, elephants don't have air sacs or pneumatic postcranial bones, so a big sauropod would certainly have been less dense (but stupider).

BTW, the whale and elephant are in good lateral views, but the brachiosaur is foreshortened and that messes up the apparent proportions. The neck length is actually half again as long as the shoulder height, and the tail is about the same length as the neck. When you look at the composite photo, just imagine that the brachiosaur's tail is sticking out over the asphalt, and is not at all parallel to the whale's backbone.

Using the "stack of Mike" method, we found a shoulder height of 18 feet for the mounted Brachiosaurus. That fit well with what we've seen mentioned other places. If this Brachiosaurus was an elephant, it would have weighed 35 tons (1.8 cubed = 5.832, multiply that by six tons). For such a goofy method, that's a surprisingly satisfying answer. Colbert (1962) and Gunga et al. (1995) used volumetric methods and estimated the mass of Brachiosaurus at 78-80 tons, but in both cases the models are grotesquely obese, more like Macy's parade balloons than real animals. Alexander (1989) got 47 tons, but his model was also too fat, as Paul (1997) very convincingly demonstrated. Russell et al. (1980) used a limb regression equation to put the mass of Brachiosaurus at 15 tons. That just makes no sense. If a 13-foot-tall elephant weighs 13 tons, then an 18-foot-tall Brachiosaurus weighed a damn sight more than 15 tons. Anderson (1985) used limb bone regression and got 29 tons. Paul (1997) used volumetrics and got 32. Henderson (2003) used a digital volumetric model with realistic air sacs and got 26. Our 35 ton estimate is in pretty good company.

When we first cranked through these numbers last July, I wrote to Mike,

We can clearly disregard Russell's 15-ton estimate as crap, and anything over about 40 tons is ludicrous for that skeleton.

To which he replied,

Yes to 15 tonnes. I would not be so quick to dismiss over-forty estimates. Consider where the "shoulder" is. On the elephant, if you're talking about the highest point on the back -- which is a fairer comparison than the elevated head/neck -- then the height is maybe a little less than 10 feet. And it doesn't need to be much less to make a big difference. Six inches shorter, in fact, would bring the BOBA [Boring Old Brachiosaurus Altithorax] estimate up to 41 tonnes. Throw in the tail and I don't find 40 too extreme. (Dude!)

What is there left to say? This is the kind of thing I spend my time thinking about. And it illustrates a couple of points that you should always keep in mind:

One last thing. None of the animals in the picture are record-holders. As I mentioned in the last post, the whale is, at 87 feet, about 80% of the size of the largest known individuals. The Brachiosaurus skeleton is about 85% of the size of the largest known specimens in the genus, and the elephant is 77% of the size of the world record. What a pathetic bunch of losers!